The invention relates to a blade for a blade row of a turbomachine having wired sections, in particular a blade of a compressor rotor blade, as well as a method for wiring sections of such a blade.
In particular in order to adapt individual sections in the radial direction to flow conditions that vary radially over a channel height of a blade row, especially the flow vectors at the inlet and outlet, building up the three-dimensional geometry (3D geometry) of a blade from successive sections in the radial direction, preferably 2D sections, i.e., wiring the sections, is known, for example from the applicant's EP 0 798 447 A2 and DE 10 2006 055 869 A1. Both these publications, along with DE 10 2005 042 115 A1, DE 34 41 115 C1 and DE 10 2005 025 213 A1, are concerned with the geometry of the individual sections, in particular the skeleton lines thereof.
Especially in the case of compressor rotor blades having a sweep in the axial direction, lateral bending stress occurs in the blade as a result of wiring in the peripheral direction, i.e., with sections that are offset from one another in the peripheral direction.
Therefore, the object of the present invention is making available an improved blade for a blade row of a turbomachine.
According to the invention, sections of a blade are wired in such a way that a first central component of a second section is selected according to at least one central component of a first section.
The central point of a section may in particular be the position rc of the mid-point of its area
                                          [                                                                                x                    C                                                                                        r                    C                                                                                        Θ                    C                                                                        ]                                ︸                          r              C                                      =                              1            F                    ⁢                                    ∫              F                        ⁢                                          r                dF                            ·                                                          ⁢                              ⅆ                F                                                                        (        1        )            with components xc in the axial direction, rc in the radial direction and ΘC in the peripheral direction and the vector rdF for the infinitesimal element dF of the section area F, preferably the position rCG of its center of mass or center of gravity
                                          [                                                                                x                    CG                                                                                        r                    CG                                                                                        Θ                    CG                                                                        ]                                ︸                          r              CG                                      =                              1            M                    ⁢                                    ∫              M                        ⁢                                          r                dM                            ·                                                          ⁢                              ⅆ                M                                                                        (                  1          ′                )            with the vector rdM for the infinitesimal mass element dM and the corresponding central component xCG in the axial direction, rCG in the radial direction and ΘCG in the peripheral direction, wherein reference is made in particular to a standard coordinate system, whose axial coordinate aligns with a longitudinal axis of the flow grid or of the turbomachine.
According to the invention, at least one of these components, which, for purposes of a more compact representation, is called the first central component, is now selected, preferably recursively, for a second section in accordance with one or more central component of a first section that is preferably preceding radially outwardly in the radial direction, i.e., a radially inward first section. This makes a wiring of subsequent sections possible in an optimal manner with respect to the central points thereof.
In doing so, according to a preferred embodiment, the individual sections, in particular the geometry or outer contour thereof, are first of all configured, preferably optimized, fluid dynamically, in particular aerodynamically, and then wired according to the invention, i.e., according to central points of a preceding section. In this way, it is possible to do justice to both fluid dynamics as well as strength demands separately and therefore optimally.
According to a preferred embodiment, a first central component of the second section selected according to the invention is also selected according to its graduated angle and/or according to a graduated angle of the first section. In this case, the graduated angle at the blade-starting side or at the blade-end side or the angle enclosing a chord between the blade leading edge and the blade trailing edge or a profile skeleton line with a row plane of the blade row is designated in a standard manner as the graduated angle or blade angle β of a section.
Additionally or alternatively, the first central component of the second section may also be selected according to at least one other, second central component of the second section. For example, it is possible, for instance for fluid dynamic reasons, to first determine an axial central point, i.e., a central component in the axial direction, for the second section and then select its central peripheral position, i.e., its central component in the peripheral direction, also according to this axial central point.
If, for example, the center of mass or the center of gravity of a radially inner first section (i) is known by its location or position xCG(i) in the axial direction, rCG(i) in the radial direction and ΘCG(i) in the peripheral direction as well as its graduated angle β(i), and the axial and radial position xCG(i+1), rCG(i+1) of the center of mass of a radially subsequent second section (i+1) as well as its graduated angle β(i+1) are given, for instance based on fluid dynamic conditions, then according to a preferred embodiment, the central peripheral position ΘCG(i+1) of the second section (i+1) obeys at least approximately the relation:
                                          Θ                          CG              ⁡                              (                                  i                  +                  1                                )                                              =                                    Θ                              CG                ⁡                                  (                  i                  )                                                      +                          Arctan              ⁡                              [                                                                            2                      ·                                              (                                                                              x                                                          CG                              ⁡                                                              (                                                                  i                                  +                                  1                                                                )                                                                                                              -                                                      x                                                          CG                              ⁡                                                              (                                i                                )                                                                                                                                    )                                                                                    (                                                                        r                                                      CG                            ⁡                                                          (                                                              i                                +                                1                                                            )                                                                                                      +                                                  r                                                      CG                            ⁡                                                          (                              i                              )                                                                                                                          )                                                        ·                                      tan                    ⁡                                          (                                                                                                    β                                                          (                                                              i                                +                                1                                                            )                                                                                +                                                      β                                                          (                              i                              )                                                                                                      2                                            )                                                                      ]                                                    ,                            (        2        )            where “tan” and “arctan” designate in standard nomenclature the tangent or the arc tangent of an angle. One can see that the offset (ΘCG(i+1)−ΘCG(i)) of the center of gravity of the second section from the first section in the peripheral direction depends on the offset (xCG(i+1)−xCG(i)) in the axial direction as well as a mean value (rCG(i+1)+rCG(i))/2 for the radial position and an averaged graduated angle (βCG(i+1)+βCG(i))/2.
It is preferred that essentially all sections of the blade obey this relation at least approximately. In particular, in order to equalize local stress, it may be advantageous, however, if radially inward sections deviate herefrom. Therefore, preferably at least radially outward sections meet the above relation, in particular all sections starting from 35% of a channel height of the blade row, preferably starting from 25% of the channel height upwards.
For simplification, instead of the mean value (rCG(i+1)+rCG(i)/2, the radial position rCG(i) or rCG(i+1) of the first or second sections may be used so that the central component ΘCG(i+1) of the second section (i+1) at least approximately obeys for example the relation:
                              Θ                      CG            ⁡                          (                              i                +                1                            )                                      =                              Θ                          CG              ⁡                              (                i                )                                              +                      Arctan            ⁡                          [                                                                    (                                                                  x                                                  CG                          ⁡                                                      (                                                          i                              +                              1                                                        )                                                                                              -                                              x                                                  CG                          ⁡                                                      (                            i                            )                                                                                                                )                                                        (                                          r                                              CG                        ⁡                                                  (                                                      i                            +                            1                                                    )                                                                                      )                                                  ·                                  tan                  ⁡                                      (                                                                                            β                                                      (                                                          i                              +                              1                                                        )                                                                          +                                                  β                                                      (                            i                            )                                                                                              2                                        )                                                              ]                                                          (                  2          ′                )            
Additional or alternatively, the graduated angle β(i) or β(i+1) of the first or second section may also be used approximately so that the central component ΘCG(i+1) of the second section (i+1) at least approximately obeys for example the relation
                              Θ                      CG            ⁡                          (                              i                +                1                            )                                      =                              Θ                          CG              ⁡                              (                i                )                                              +                      Arctan            ⁡                          [                                                                    (                                                                  x                                                  CG                          ⁡                                                      (                                                          i                              +                              1                                                        )                                                                                              -                                              x                                                  CG                          ⁡                                                      (                            i                            )                                                                                                                )                                                        (                                          r                                              CG                        ⁡                                                  (                                                      i                            +                            1                                                    )                                                                                      )                                                  ·                                  tan                  ⁡                                      (                                          β                                              (                                                  i                          +                          1                                                )                                                              )                                                              ]                                                          (                  2          ″                )            
For example, in order to equalize fluid forces, in particular gas forces, the blade may be inclined in the circumferential direction by the angle Θlean. Then the following term may be added to the central component ΘCG(i+1) of the second section (i+1) according to one of the relations explained in the foregoing:
                    Arcsin        ⁡                  [                                                    (                                                      r                                          CG                      ⁡                                              (                                                  i                          +                          1                                                )                                                                              -                                      r                                          CG                      ⁡                                              (                        1                        )                                                                                            )                                            (                                  r                                      CG                    ⁡                                          (                                              i                        +                        1                                            )                                                                      )                                      ·                          sin              ⁡                              (                                  Θ                  lean                                )                                              ]                                    (        3        )            so that the central component ΘCG(i+1) of the second section (i+1) at least approximately obeys the relation:
                                          Θ                          CG              ⁡                              (                                  i                  +                  1                                )                                              =                                                                      Θ                                      CG                    ⁡                                          (                      i                      )                                                                      ++                            ⁢                              Arctan                ⁡                                  [                                                                                    2                        ·                                                  (                                                                                    x                                                              CG                                ⁡                                                                  (                                                                      i                                    +                                    1                                                                    )                                                                                                                      -                                                          x                                                              CG                                ⁡                                                                  (                                  i                                  )                                                                                                                                              )                                                                                            (                                                                              r                                                          CG                              ⁡                                                              (                                                                  i                                  +                                  1                                                                )                                                                                                              +                                                      r                                                          CG                              ⁡                                                              (                                i                                )                                                                                                                                    )                                                              ·                                          tan                      ⁡                                              (                                                                                                            β                                                              (                                                                  i                                  +                                  1                                                                )                                                                                      +                                                          β                                                              (                                i                                )                                                                                                              2                                                )                                                                              ]                                                      +                          ,                  +                      Arcsin            ⁡                          [                                                                    (                                                                  r                                                  CG                          ⁡                                                      (                                                          i                              +                              1                                                        )                                                                                              -                                              r                                                  CG                          ⁡                                                      (                            1                            )                                                                                                                )                                                        (                                          r                                              CG                        ⁡                                                  (                                                      i                            +                            1                                                    )                                                                                      )                                                  ·                                  sin                  ⁡                                      (                                          Θ                      lean                                        )                                                              ]                                                          (                                            2              ′                        ′                    ′                )            
Additional features and advantages are disclosed in the subordinate claims and the exemplary embodiment.